Continuous-time vs discrete time identification?

Hi,

I have a real plant that I'm sampling with 0.001 interval. For this reason all the measurement data in my Matlab are vectors that include data from every 1ms.

I have also constructed a state-space model for my real plant and I want to do greybox-modelling and thus identify some parameters of my real plant by using the measurement data.

I'm wondering now, should I do the parameter identification for a continuous-time state-space model of the plant, or for a discrete state-space model (discretized with 1ms sample time)? The real world is continuous, but the measurements from the plant are "discrete" as I have them only with 1ms interval. Thus, which is better, to use the measurement data to identify parameters for a continuous or discrete time state-space model?

Additionally, I do a idgrey model of my state-space model. Should I construct this idgrey model based on continuous-time model of the plant, or discretized model of the plant? The discrete-time idgrey model needs the "sampletime Ts" as input in order to produce the idgray object. Does the idgray-function discretize the model with the given sampletime and return the discretized grey-box model? Or is the "Ts" only used for metadata that is included into the idgrey object's data?

Thanks for any ideas for declaring this.

Cheers, Joonas

Answer 1

[Simone Pirrera]

Grey-box identification problem can be posed both in continuous and discrete-time. Depends on the physics of your system: most commonly plants are described as differential equations and therefore you have continuous-time models.

I can suggest you to read this article for a nice grey-box identification procedure that applies both to DT and CT models

O. Prot and G. Mercère, "Combining Linear Algebra and Numerical Optimization for Gray-Box Affine State-Space Model Identification," in IEEE Transactions on Automatic Control, vol. 65, no. 8, pp. 3272-3285, Aug. 2020, doi: 10.1109/TAC.2019.2942567.